Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulationsU. Thiele1, L. Brusch1, M. Bestehorn2 and M. Bär1
1 Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
2 Lehrstuhl für Statistische Physik und Nichtlineare Dynamik, BTU-Cottbus, Erich-Weinert-Strasse 1, D-03046 Cottbus, Germany
(Received 29 January 2003 and Received in final form 6 May 2003 / Published online: 15 July 2003)
We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.
68.15.+e - Liquid thin films.
81.16.Rf - Nanoscale pattern formation.
47.20.Ky - Nonlinearity (including bifurcation theory).
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003